Compression and shear of a layer of granular material

Spencer, A. J. M.

doi:10.1007/s10665-004-5662-9

Cited by 9 publications

(6 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The asymptotic analysis of these solutions shows that they satisfy (33), ( 34), (36) and (38). Several semi-analytic solutions for the double-shearing model, which is another widely used model of pressure-dependent plasticity, have been derived in [11][12][13] and [16]. The asymptotic analysis of these solutions also shows that they satisfy (33), ( 34), (36), and (38).…”

Section: Plane Strain Deformationmentioning

confidence: 99%

“…A distinguished feature of this boundary condition is that the regime of sliding occurs independently of the friction law chosen. In the case of pressure-dependent plasticity, such solutions have been found in [11][12][13]. In these works, the double shearing model proposed in [14] has been adopted.…”

Section: Introductionmentioning

confidence: 99%

“…In these works, the double shearing model proposed in [14] has been adopted. The solutions given in [11][12][13] show that the velocity field is singular (some derivatives approach infinity in the vicinity of envelopes).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solution Behavior in the Vicinity of Characteristic Envelopes for the Double Slip and Rotation Model

2020

View full text Add to dashboard Cite

The boundary conditions significantly affect solution behavior near rough interfaces. This paper presents general asymptotic analysis of solutions for the rigid plastic double slip and rotation model in the vicinity of an envelope of characteristics under plane strain and axially symmetric conditions. This model is used in the mechanics of granular materials. The analysis has important implications for solving boundary value problems because the envelope of characteristics is a natural boundary of the analytic solution. Moreover, an envelope of characteristics often coincides with frictional interfaces. In this case, the regime of sticking is not possible independently of the friction law chosen. It is shown that the solution is singular in the vicinity of envelopes. In particular, the profile of the velocity component tangential to the envelope is described by the sum of the constant and square root functions of the normal distance to the envelope in its vicinity. As a result, some components of the strain rate tensor approach infinity. This finding might help to develop an efficient numerical method for solving boundary value problems and provide the basis for the interpretation of some experimental results.

show abstract

Section: Plane Strain Deformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solution Behavior in the Vicinity of Characteristic Envelopes for the Double Slip and Rotation Model

2020

View full text Add to dashboard Cite

show abstract

“…This study also provides solutions for the stress field and proceeds to develop the velocity field using the velocity equations for granular materials proposed by Spencer [1964]. The problem of the combined compression and shear of a thin layer of granular material was also examined in an elegant analytical study by Spencer [2005]. Unfortunately, when the results are applied to the study of the compression of a granular layer, a necessary requirement is knowledge of the stresses that are applied at the boundary edges of the thin layer to maintain the integrity of the granular layer.…”

Section: Auxiliary Problem IImentioning

confidence: 99%

Proppant-Induced Opening of Hydraulically Created Fractures

Selvadurai¹

2019

Open Geomechanics

View full text Add to dashboard Cite

The paper examines the problem of the open configuration created when a hydraulic fracture fluid containing a granular proppant is introduced into the fracture. The mathematical modelling examines the problem of an extended cracked region that is wedged open by a granular material present over a finite region of the crack. The combination of the geostatic stress state and the contact stress created between the granular proppant and the elastic rock mass is used to develop a consistency relationship for estimating the dimension of the region of the fracture that will remain open when the pressures applied to create the fracture are released. The interactive mechanics of the fracture and the proppant has an influence on the geometry of the open region that provides the pathway for extraction of the resource.

show abstract

“…This feature of solution behavior has been demonstrated in [8] for rigid perfectly-plastic material and in [9,10] for viscoplastic material with a saturation stress. Additionally, numerous analytic and semi-analytic solutions for various material models reveal this behavior of solutions [1,2,11,12,13,14,15]. It is evident that numerical solutions of the corresponding boundary value problems do not converge [16,17,18], unless a special technique is adopted (for example, [19,20]).…”

Section: Introductionmentioning

confidence: 99%

Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers

et al. 2019

View full text Add to dashboard Cite

The present paper deals with plane strain deformation of incompressible polymers that obey quite a general pressure-dependent yield criterion. In general, the system of equations can be hyperbolic, parabolic, or elliptic. However, attention is concentrated on the hyperbolic regime and on the behavior of solutions near frictional interfaces, assuming that the regime of sliding occurs only if the friction surface coincides with an envelope of stress characteristics. The main reason for studying the behavior of solutions in the vicinity of envelopes of characteristics is that the solution cannot be extended beyond the envelope. This research is also motivated by available results in metal plasticity that the velocity field is singular near envelopes of characteristics (some space derivatives of velocity components approach infinity). In contrast to metal plasticity, it is shown that in the case of the material models adopted, all derivatives of velocity components are bounded but some derivatives of stress components approach infinity near the envelopes of stress characteristics. The exact asymptotic expansion of stress components is found. It is believed that this result is useful for developing numerical codes that should account for the singular behavior of the stress field.

show abstract

Compression and shear of a layer of granular material

Cited by 9 publications

References 16 publications

Solution Behavior in the Vicinity of Characteristic Envelopes for the Double Slip and Rotation Model

Solution Behavior in the Vicinity of Characteristic Envelopes for the Double Slip and Rotation Model

Proppant-Induced Opening of Hydraulically Created Fractures

Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers

Contact Info

Product

Resources

About